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Drag
Continuum Mechanics Definition ] A body moving through a fluid is submitted to an interaction between its outer surface and the fluid. This can be described as a force including two terms : * the wall shears stresses, due to viscous effects Tw * the normal stresses due to pressure p'' The integrated or resultant aerodynamic effects of these distributions can also be splitted in two terms: lift and drag. The drag is the resultant force in the direction of the upstream velocity ''U relative to the airfoil. Considering an aircraft, drag is instantaneously tangent and opposite to its flypath.1 Commonly used Equation In aerospace engineering, the overall drag is generally expressed as follows: Types of Drag Three types of drags are usually distinguished, including themselves different components: *parasite drag *lift induced drag *wave drag Parasite drag Parasite drag (also called parasitic drag or zero-lift drag) is made up with multiple components including : *form drag : pressure-type loss due to the shape of the wetted surface *skin friction drag : viscous-type loss due to the wetted surface roughness *interference drag : the proximity of several bodies creates mutual interferences in the air flow around each different elements. A well designed aircraft in subsonic flight will have a parasite drag mostly due to skin friction plus a small separation pressure drag. The parasite drag coefficient is denoted CDmin or CDo as it describes the minimum possible drag the aircraft would be faced with, when no lift is produced at a subsonic velocity. Lift-induced drag Lift-induced drag is the result of lift creation on a three-dimensional lifting body, such as wings or fuselage of an airplane. Lift-induced drag includes the creation of vortices above the wings as well as the additional viscous drag. The lift-induced drag coefficient is CDi and is approximated to vary proportionally to the square of the lift coefficient CL. 2 where AR is the aspect ratio (wingspan squared over the wing area) Since its calculation is based on the area of the wing S, the expression of the lift-induced drag must be completed by the trim drag. This additional drag is caused by the horizontal tail (or canard) force that is instantaneously required to balance the aircraft total pitching moment around its center of gravity. Wave drag Wave drag (also called compressibility drag) only appears in transonic and supersonic flights. The transonic flow regime extends from about Mach 0.8 to 1.2. As an airplane accelerates through the transonic regime the increase of drag is due to the formation of shocks. A shock is the supersonic phenomenon. Though, even if the aircraft is flying at a subsonic speed some areas of its fuselage may encounter a supersonic airflow . This is especially true above the wings where the airflow is strongly accelerated. Two Mach Number are then defined: *the critical Mach number Mcr ''is the dimensionless velocity at which shocks first form on the airplane. *the drag divergent Mach number '''MDD at which the formation of shocks begins to significantly affect the drag. For instance, Boeing definition is '''''MDD = 1.08 Mcr. 3 Influence of Mach and Reynolds numbers The drag coefficient depends largely on the velocity of the flow. Since the Mach number and the Reynolds number vary both proportionally with the airflow speed, drag can be seen as a function of both Re and Ma.1 If the Mach number M < 0.5, then CD is mostly a function of Re. For streambodies like a wing, the drag coefficient increases when the boundary layer surrounding it becomes turbulent because most of the drag is due to the shear force. So the drag increases with the flow speed, and the surface roughness of the wing. Indeed, the surface roughness of the wing will decreases the Reynolds number at which the boundary layer becomes turbulent. On the other hand, if the velocity is large enough, compressibility effects have to be taken into account. CD becomes then essentially a function of Ma. CD increases generally dramatically in the vicinity of Ma = 1. A sharp wing would see its CD being maximum around Ma = 1 whereas a more blunt airfoil would see its maximum CD right before Ma = 1. That is why the leading edges of wings for subsonic aircraft are more rounded and blunt than those of a supersonic aircraft, being more pointed and sharp. References *''Fundamentals of Fluid Mechanics'', 5th Ed, M.Y. Okiishi, Wiley Publications, p. 485-486 *''Dynamics of Atmospheric Flight'','' Bernard Etkin, Dover Publications, p. 198 *''Aicraft Design: A Conceptual Approach, 4th Ed, Daniel P. Raymer, AIAA, p. 327-347 *http://www.aerospaceweb.org/question/aerodynamics/q0184.shtml Category:Things You Should Know Category:Aerodynamics Category:Aircraft Design